# De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity. (arXiv:1709.03513v2 [hep-th] UPDATED)

We investigate the proposed connection between de Sitter spacetime and the

MERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and ask

what can be learned via such a construction. We show that the quantum state

obeys a cosmic no-hair theorem: the reduced density operator describing a

causal patch of the MERA asymptotes to a fixed point of a quantum channel, just

as spacetimes with a positive cosmological constant asymptote to de Sitter. The

MERA is potentially compatible with a weak form of complementarity (local

physics only describes single patches at a time, but the overall Hilbert space

is infinite-dimensional) or, with certain specific modifications to the tensor

structure, a strong form (the entire theory describes only a single patch plus

its horizon, in a finite-dimensional Hilbert space). We also suggest that de

Sitter evolution has an interpretation in terms of circuit complexity, as has

been conjectured for anti-de Sitter space.